Laser Experiments and Projects Introduction

This chapter provides a variety of suggestions for experiments and projects
using lasers ranging from trivial to quite advanced. Some utilize the optical
properties of the laser beam like its ability to be well collimated or highly
focused while other depend on the unique coherence and monochromicity of the
laser light itself. And still others take advantage of the ability to
modify or control the lasing process via intra-cavity optical components,
magnetic fields, or other mechanisms.

Currently, they are just suggestions. (If you can't wait, there are also some
links to Web sites with educational laser projects below.) Eventually,
additional details of the setup and required supplies will be added.
Where the particular topic is already discussed elsewhere in Sam's Laser FAQ,
a link to that section will be provided. However, in most cases, at least
some of the details will be left as an exercise for the student. What fun
or challenge would it be if we told you everything? After all, besides
its educational value, hands-on experience should indeed be
both fun and challenging! However, where more information is available in
this document, links are provided.

A 1 to 5 mW internal mirror helium-neon laser will be suitable for most of the
basic experiments (though a somewhat higher power one would be better for
those like holography). It should be possible to procure such a laser for
under $50, possibly under $25 depending on your resourcefulness and scrounging
abilities.

Some experiments may require a polarized laser but for most, any type will
do, even a better quality (one with an adjustable focusing lens) laser
pointer - and those are practically given away in cereal boxes these days. :)
Where access to the laser cavity is required, an external mirror HeNe or Ar/Kr
ion laser will be needed. A one-Brewster HeNe laser setup can be put together
quite inexpensively (probably under $100) using a surplus one-Brewster HeNe
tube and power supply, the OC mirror from a deceased HeNe laser, and some
scrap materials available in any well equipped junk box. Of course, if
you have access to a nice lab laser, that would be fine as well but probably
not nearly as much fun or as rewarding compared building one (at least
partially) yourself. :)

Alternatives like bare laser diodes and appropriate drive circuitry may be
more desirable for projects like laser communications where modulation is
required. And, other color lasers (than the boring red HeNe or laser pointer)
will be desirable for laser display.

The material in this chapter has been derived from various sources including:

A tutorial from Electro Optics Associates, whoever they were. My
apologies if they evolved into one of the major laser manufacturers! This
booklet was apparently provided along with an early external mirror HeNe
laser (LAS101) for educational purposes. This had a wide bore tube running
on only 300 VDC with a resonator length of about 14 inches. The mirrors
could be interchanged to produce a multimode or TEM00 beam. While this is
from a booklet dated 1965 (!!), all the experiments are still quite valid.

All of these experiments can be performed with a fully enclosed 1 mW
HeNe laser (or laser head and power supply) which poses minimal risk to vision
and no shock hazard from even gross carelessless (though not totally, perhaps,
from deliberate abuse). However, some, like those dealing with holography,
could benefit from a 5 mW or larger laser. Higher power lasers, especially
those above 5 mW, need to be treated with great respect as even momentary eye
exposure can cause permanent damage to vision.

In addition, those experiments requiring access to the interior of the
resonator of an external mirror laser may expose the user to potentially
lethal voltages in the vicinity. If possible, any exposed high voltage
terminals should be well insulated or blocked from accidental access. And,
where all you have is an exposed HeNe laser tube and separate power supply,
building all this into a safe enclosure is highly recommended.

Read the chapter: Laser Safety in its entirety
and follow its guidelines - particularly in regards to the safety of others
who may not be as aware as you in dealing with your equipment.

Basic Experiments with Lasers

When neutral density filters are placed one after the other, their ND numbers
(-log attenuation) add. So two ND1 filters (T = .1) in series results in a
equivalent ND2 filter (T = .01).

Now, what happens if multiple dielectric mirrors are placed in series? Under
certain condition, more light will get through than might be expected. For
example, using the same example as above, if T = .1 for both mirrors, the
resulting output may actually be as high as for an equivalent mirror with
T = .05 (rather than T = .01). Why? Under what conditions will this happen?
How does the T factor of each mirror affect this behavior? What other factors
are important?

Diffraction and Interference

This just requires a pair of narrow closely spaced slits, a
laser pointer or HeNe laser, and a screen or white card onto
which to project the resulting diffraction pattern. The main
problem is in getting the slits to be narrow and close enough
together to obtain a nice wide pattern.

(From: Skywise.)

I once made a two slit experiment using a piece of glass, two razor
blades, some tape, and some water based acrylic paint.

First I painted the glass with the paint. I chose a dark green color
which absorbed my HeNe light pretty well. To make a smooth single layer
of paint I put two parallel strips of Scotch tape on the glass about
1/2 inch apart. Then I placed a drop of paint towards one end of
the channel formed by the two pieces of tape. With a razor blade resting
on the tape, I dragged the blade along the channel thus spreading a
nice thin even coating of paint along the glass. With practice on how
much pressure to apply I was able to get a very good strip of paint
that wasn't too thick or thin.

While the paint dried I taped two razor blades stacked together. To
get the razor edges closer together than the thickness of the blades
I used a small piece of folded paper at the back edge of the blades
so as to fulcrum the sharp edges of the blades closer together.

Once the paint was dried I quickly dragged the two points on the corner
of the joined blades across the paint strip thus creating two parallel
slits.

With practice on applying the paint, adjusting the gap of the blades,
amount of pressure when scoring the paint, etc... I was able to
successfully make two slits close enough that a raw beam from my
5 mW HeNe pointed at the two closely spaced slits caused diffraction
in the far field.

It was quite fun and was very useful for demonstrating the wave
nature of light.

The objective here would be relate the visible wavelengths in the discharge
inside the bore to the actual output wavelengths. For example, while red
at 632.8 nm is the strongest of the visible HeNe wavelengths, it is a
relatively weak line int he discharge. A long HeNe laser with external
interchangeable or multi-line optics, or a tunable (e.g., PMS/REO) HeNe
laser would be best for this experiment.

Experiments Inside the Laser Cavity

These require access to a laser with at least one external mirror. The
usual choice would be a modest size lab type HeNe laser. Unfortunately, these
aren't the sort of thing one typically has at home. And, even if you find
one, it may not be convenient (or permitted if it isn't yours!) to gain access
to the cavity. However, it is possible to put together something that is
every bit as good for minimal cost using a HeNe laser head with an internal
HR mirror and Brewster window at the other end. A HeNe laser power supply
and easy to construct mirror mount completes the assembly which provides full
access to the inside of the cavity between the Brewster window and external
mirror. One-Brewster HeNe tubes and laser heads are available on the surplus
market but you may have to ask. As an example of such a laser head, see the
section: A One-Brewster HeNe Laser Tube.
A complete laser using this laser head is described in the section:
Sam's Instant External Mirror Laser Using a One
Brewster HeNe Tube. One-Brewster tubes, heads, a complete kit with
power supply, as well as a mirror assortment, are available on
Sam's Classified Page.

The setup described in the section:
Mirror/Optics Test Jig Using One-Brewster HeNe
Laser Tube may be used to perform a variety of experiments requiring
access to the inside of an adjustable length resonator using various
mirrors or other optics. With the commonly available one-Brewster HeNe laser
tubes like the Melles Griot 05-LHB-570, either multimode or single mode
operation is possible depending on the external configuration.

Here are some suggested experiments and questions to ponder using this rig:

How does the mode structure vary with L?

How does the mode structure vary with OC curvature?

How does the mode structure vary with OC alignment?

How is the sharpness of the mode structure affected by OC quality (e.g.,
comparing a laser mirror to a barcode scanner mirror)?

How does the divergence vary with L?

Can a positive lens always focus the multimode beam to a small spot?

How does the profile of the intra-cavity beam (mode volume) change with
L?

What effect does a variable stop (iris), knife edge, or arbitrary pattern
placed inside the cavity have on the output beam? How is this affected by
position? What about at the Brewster window or OC surface?

How does output power vary with L (assuming the OC alignment is tweaked
for maximum power at each location)?

The optogalvanic effect is a phenomenon whereby the electrical
conductivity of a gas discharge is affected by light (generated
or external) that is resonant with an atomic or molecular transition
of the elements within it. One application is in spectroscopy
whereby gas composition can be determined by illuminating the discharge
a tunable light source while recording its voltage or current.

The optogalvanic effect can be observed even with a normal HeNe laser
without external illuviation. As the tube warms up, the longitudinal
modes shift through the gain curve and and the output power - and thus
the intracavity power - changes depending on where the modes are.
For long healthy tubes, the change is small. But for short tubes
especially where the output power typically varies by 20 percent
or more, it is easy to see as the sustaining voltage changing in
synchrony with the power fluctuations.

If the HeNe laser power supply is constant current, as with most commercial
units, the sustaining voltage will have to be monitored.
Connect an oscilloscope through a 10 nF or larger high voltage capacitor
to the top of the ballast resistor. Even being AC coupled, the voltage
will be seen to move up and down perhaps a few 100s of mV or more as the
power changes. CAUTION: Make sure the scope input is protected from the
high voltage!!!! :) I use an NE2 neon lamp across the scope input to limit
the voltage to 90 V even during transients.

If the power supply is unregulated, then the current will change as the
tube's sustaining voltage changes, and this can most easily be monitored
as the voltage across a resistor in series with the tube's negative return.

Advanced Laser Experiments

A Scanning Fabry-Perot Interferometer (SFPI) consists of a pair
of partially reflective mirrors. The laser under test (LUT) is input to
one end and a photosensor is mounted beyond the other end. The
coarse spacing and alignment of the mirrors can be adjusted by
micrometers. The axial position of one of the mirrors can be varied
very slightly by a linear PieZo Transducer (PZT).
By driving the PZT with a triangle waveform and watching
the response of the photosensor on an oscilloscope, the longitudinal
modes of the LUT can be displayed in real time. In essence, the comb response
of the SFPI is used as a tunable filter to analyze the fine detail of the
optical spectrum of the LUT. As long as the FSR (c/2*L) of the SFPI
is larger than the FSR of the LUT (i.e., the SFPI cavity is shorter than
the LUT cavity), the mode display will be unambiguous.

Assuming a function generator and oscilloscope are available,
it is possible to build an SFPI that demonstrates basic principles for
next to nothing, or one that rivals the performance of commercial
instruments costing many thousands of dollars for less than $100. See
the sections starting with Sam's $1.00 Scanning
Fabry-Perot Interferometer. Even this very simple SFPI using salvaged
mirrors will easily resolve the longitudinal modes of a HeNe laser.
I offer sets of mirrors suitable for a confocal HeNe laser mode display
SFPI. See Sam's Classified
Page under "HeNe Laser Kits".

By adding an external mirror or grating to a conventional internal mirror
red or other color HeNe laser tube, it is usually possible to get anywhere
from 1 to over a dozen other lasing wavelengths to appear. With am aluminized
or dielectric mirror next to the OC, even a 1 mW red (632.8 nm) tube will
probably give 1 or 2 additional red lines. With a 3 to 5 mW tube, 4 or 5,
or even more may be produced. Some of these are not normal HeNe laser lines
and their existence is not widely known. In fact, being able to do this
overall experiment isn't something that's widely known. See the section:
Getting Other Lasing Wavelengths from Internal
Mirror HeNe Laser Tubes.

Commercial, very expensive stabilized HeNe lasers are actually quite
simple in principle and can be built from mostly junk parts. With
care, the performance of these systems can rival that of units costing
thousands of dollars.

All that is needed is a short HeNe laser tube to which a heater has been
added, some optics and photodiodes to sample the amplitude of either one
mode polarization or two mode (orthogonal) polarizations, and some
basic electronic components to implement the control loop.

I may be able to provide a set of parts including a well behaved HeNe laser
tube, HeNe laser power supply, beamsplitter(s), photodiodes. Some
mechanical skills will be required to mount everything. The electronic
components can be obtained from places like Digikey or Jameco.

Using a 5 mW or larger TEM00 polarized HeNe laser and high speed
silicon photodetector, it is possible to monitor the difference frequencies
resulting from longitudinal mode beating as well as the differences of the
difference frequencies, which are non-zero due to mode pulling. See the
sections starting with: Longitudinal Modes
of Operation.

For looking at the longitudinal mode beating, a photodetector and
oscilloscope with a response beyond c/2L for the HeNe laser will be
required. This would be 500 MHz for a 12 inch long tube (mirror
to mirror). So a longer tube would be desirable both due to its
lower beat frequencies and more modes. For the second order
difference frequencies, the photodetector still has to be fast but
the scope only needs to respond to 100 kHz or so.

The setup is similar to that for longitudinal modes beating, above, except
that a multimode (non-TEM00) HeNe laser is required. The response of both
the photodetector and oscilloscope only needs to be a few MHz since
transverse modes are quite close together in frequency. A lens may be
needed to force overlap of the mode spots since they won't mix if falling
on separate areas of the photodetector.

Experiments that explore the effect of a magnetic field on the behavior
of a HeNe laser can be extremely fascinating for a hobbyist-experimenter
type. This is due to how dramatically the fundamental operation of the
laser with respect to longitudinal modes and polarization are affected
by external permanent magnets or an electro-magnet.
In addition to a 1 to 2 mW random polarized HeNe laser, only
very basic equipment and common low cost readily available optics
and electronic parts are needed. Data can be recorded using a $25
PC-based data acquisition system or even a simple chart recorder.

There are at least two arrangements primarily differing whether the
magnetic field is oriented along the optical axis of the tube (axial)
or perpendicular to it (transverse). Of course, no law prevents
experimenting with the field at other orientations!

All that is needed to explore axial Zeeman splitting is
a random polarized HeNe laser tube (5 to 6 inches is
probably optimal) and power supply, a ring magnet into which the HeNe laser
tube can be placed producing an axial magnetic field (or electromagnetic
solenoid), a photodetector with a response to a couple of MHz, and an
oscilloscope. See the section: Two
Frequency HeNe Lasers Based on Zeeman Splitting for more information.

Here is a summary of the basic procedure for Zeeman splitting using an
axial magnetic field. The following components are required:

HeNe laser tube: Suitable choices are tubes from Hewlett Packard
model 5501 or 5517 laser heads (with or without output optics but including
the original ring magnets), or home-built versions of these using common
non-polarized 5 or 6 inch barcode scanner HeNe laser tubes with powerful
ring magnets polarized N-S along their axis.

HeNe laser power supply: This can be the original one that went
with the laser but it is not critical as long as the tube current is
reasonably close to its specification. For these small tubes, 3.5 mA
is usually adequate.

Polarizer: Any material or optic that will act as a polarizer
at the red 632.8 nm HeNe laser wavelength. The usual choice would be a
piece of a linear polarizer sheet.

Photodetector: If the laser tube came from a commercial laser
head, the best choice is the photodiode and preamp board that was also
present there as it will have an AGC circuit and comparator to cleanup
the detected signal. Otherwise, any silicon photodiode can be used with
reverse bias to improve the frequency response. If there is no AGC,
some means of adjusting the beam intensity incident on the photodiode
will be required. This can be as simple as moving the beam position so
only a portion of it hits the detector.

Oscilloscope and/or frequency counter: Anything with a bandwidth
of at least 5 MHz will suffice.

Set up the components in a reasonably stable manner. The polarizer
just needs to be in the beam - its orientation doesn't matter since
it's simply converting circular to linear polarization.

Using a scope (preferably) or frequency counter, look for a beat frequency
from the detector. The HP 5501 tube is very stable - its frequency will only
vary by a few percent over several minutes. The frequency of the HP 5517
tube varies quite widely in a periodic manner as mode cycling takes place due
to heating. The beat may disappear totally during part of the cycle. This
behavior is very similar to that of the home-built version.

Adding some means of cavity length stabilization would be the next step.

Experiments can also be performed without the tube inside the ring magnets
by trying various positions and orientations of external magnets. It may
even be interesting to put the output through an audio amp and speaker as
the beat frequency with a smaller magnetic field will cover the audio range.

All that is needed to explore transverse Zeeman splitting is
a random polarized HeNe laser tube (9 or 10 inches is probably optimal)
and power supply, a set of moderate strength ferrite magnets with
North and South poles on the flat faces producing a transverse magnetic
field into which the HeNe laser tube can be placed, a photodiode with
a response of a few hundred kHz (almost any will do), and
an oscilloscope to observe the Zeeman beat. To also observe the
longitudinal modes, total power, and Zeeman signal amplitude, additional
photodiodes and some basic electronics will be required. A PC-based
data acquisition can then be used to record, plot, and analyze the data.
See the section:

Here is a summary of the basic procedure for Zeeman splitting using an
transverse magnetic field. The following components are required:

HeNe laser tube: Suitable choices are common longer barcode
scanner tubes like the Melles Griot 05-LHR-088, Spectra-Physics 088,
Uniphase 098. These are about 9.5 inches in length and are probably
optimal in their longitudinal mode spacing. Shorter tubes will have
a limited range (magnetic field strength and portion of mode sweep cycle)
where a beat can be observed. Longer tubes may similar problems but
due to too many modes being present.

HeNe laser power supply: This can be the original one that went
with the laser but it is not critical as long as the tube current is
reasonably close to its specification.

Polarizer: Any material or optic that will act as a polarizer
at the red 632.8 nm HeNe laser wavelength. The usual choice would be a
piece of a linear polarizer sheet. Additional polarizers will be needed
if it is desired to also observe the polarized mode amplitudes.

Photodetector: At the expected beat frequency in the 10s to 100s
of kHz range, almost any silicon photodiode can be used with
reverse bias to improve the frequency response. Some means of
adjusting the beam intensity incident on the photodiode
will be required. This can be as simple as moving the beam position so
only a portion of it hits the detector.

Oscilloscope and/or frequency counter: Anything with a bandwidth
of at least 1 MHz will suffice.

Set up the components in a reasonably stable manner. It will be necessary
to determine the natural polarization axes of the tube. Orient
the magnets their field parallel to one of the axes and the polarizer
at 45 degrees to one of the axis. Using a scope (preferably) or frequency
counter, look for a beat
frequency from the detector. Depending on magnetic field strength (i.e.,
how many magnets are used and how close they are to the tube), there will
be a beat signal over part or all of the mode sweep cycle.
Experiment with various configuration of the magnets.

To observe the polarized mode amplitudes, some additional optics for beam
sampling will be required, along with photodiodes and possibly some simple
electronics and a low speed data acquisition system to record the data.

This type of laser can also be frequency stabilized since the beat frequency
varies with mode position. A Phase Locked Loop (PLL) is generally used but
a simple Frequency-to-Voltage (F-V) converter and op-amp will work in a manner
similar to that of the polarized mode stabilized lasers.

The Faraday effect or Faraday rotation is an interaction of electromagnetic waves
with a magnetic field in transparent dielectric materials. In simple terms, the
polarization of the beam is rotated by an amount and direction proportional to the
Verdet constant for the material times the component of the magnetic field in the
direction of propagation times the length of interaction. So, the simple
(non-integral) equation would be: β = VBd, where β is the rotation
angle, V is the Verdet constant, B is the component of the magnetic field
along the direction of propagation of the beam, and d is the interaction length.

Many common materials like Nd:YAG have a small Verdet constant, though it is still
sufficient to enable a strong magnet to produce enough of an FR effect to be used
in forcing unidirectional operation of a ring laser. However, there are some special
materials with very large Verdet constants. Terbium-doped glass has V =
65 deg/(T*cm) (T = Tesla = 10,000 gauss). And Terbium Gallium Garnet
(Tb3Ga5O12 or TGG) has a Verdet constant
about twice as large.

To put this in perspective, a 2 cm long rod of terbium-doped glass will rotate
the polarization by 10 to 20 degrees if inserted inside a stack of two ferrite
magnetron magnets. Even a "refrigerator" magnet of around 100 gauss will
result in a detectable effect if the rod is between crossed polarizers or
a polarizer is used with a linearly polarized laser. And 100 degrees or
more is possible using a tabletop magnetic pulser. See the next section.

OK, this isn't in the "can crusher" or "rail gun" category, but it's capable
of a 1 Tesla pulsed field inside a small coil. That probably could be used
to "charge" ferrite and AlNiCo magnets, and maybe some types of rare
earth magnets. Well, that is, if they are quite small. The bore is only
about 3/8" in diameter. See Overall System for Testing
Faraday Rotation in Kigre M18 Glass Rod.

Pulser electronics:

The pulser dumps the energy in a charged capacitor bank using the flashlamp
from a disposable camera as the switch. I'm using an unregulated linear HeNe
laser power supply on a Variac as the capacitor charger for 5 uF at 2,000 to
2,500 V using a pair of 10 uF, 1,500 V capacitors in series with
equalizing/bleeder resistors of 1.6M ohms on each. (Actually 4,
400K ohm, 2 W resistors in series.)

WARNING: The energy stored in this capacitor bank can be quite lethal. It's
greater than that for a microwave oven capacitor.

The flashlamp has a self breakdown voltage of about 2,500 V so it alone can
make a really big relaxation oscillator. But, the breakdown voltage is not
nearly as consistent as with an NE2 neon lamp, so the rate of flashing using
self-breakdown was highly erratic. So I used some of the
remaining components from the flash unit to provide a manual trigger.
The voltage for the trigger capacitor is taken across the bottom bleeder
resistor. The single flashlamp is marginal at 2,500 V since it likes to
fire on its own - two in series would probably be better. But this way,
it lets me know not to try to push my luck at higher voltage. Most of
my subsequent tests were done at just under 2,500 V so that it would not
flash on its own. Charging requires about 15 seconds which
results in a conservative average power for the solenoid, which would
be the limiting component.

See Photo of Magnetic Pulser Flashlamp Switch and
Trigger Circuit. The neon bulb will be lit when there is more than
60 V across the flashlamp so it serves as a danger indicator. The large
blue capacitor isolates the trigger wire from the trigger transformer so
that even if the flashlamp arced to the trigger wire, it wouldn't go
any further. And note that the trigger wire isn't even near the flashlamp.
When any closer, the flashlamp would self-fire at less than 2,000 V.
The large black cylindrical object is the 0.2 ohm current
sense resistor, with a scope probe and ground clip visible attached to it.
The yellow and blue wires go to the pulser coil and the orange wires go to the
remote trigger pushbutton.

The pulser coil is from an actual magnetic solenoid used to actuate some sort
of something or other. ;-) It was carefully selected because the bore size
was correct for what had to go into it. :) With the rear pole piece drilled
out and removed, it has a nice magnetic yoke to complete the magnetic circuit
outside the bore of the solenoid. It's pure luck that this sort of thing
survives being pummeled with pulses of nearly 2,500 V, as its normal operating
voltage is 24 VDC. But so far so good.

Laser and optics:

I'm determining the magnetic field using a special type of magneto-optically
active glass (M18, available at exorbitant cost from
Kigre, though I'm sure if it's a listed
product, mine is a sample on loan). This material exhibits a
strong Faraday effect, rotating the polarization of a beam of light in
proportion to the axial component of the magnetic field. The sensitivity
of the Faraday Rotation (FR) in M18 is about 123.5 degrees per Tesla
(10,000 gauss) for the 1.9 cm long rod. And, at nearly 2,500 V, I'm
exceeding 1 T.

The very high class optical setup is shown in
Optical Setup for M18 Faraday Rotation
Experiments. Now these are true optical breadboards! :) It
consists of a polarized 5 mW HeNe laser, the M18 rod (hidden inside
the hole in the solenoid - note the piece of clear tape to prevent it from
falling out accidentally if the solenoid is tipped!), a Melles Griot
non-polarizing beamsplitter cube followed by a piece of Polaroid-type
linear polarizer for each exit, and a reverse biased $2 photodiode
with a 3.3K ohm load resistor.

While using a polarizing beamsplitter to obtain orthogonal vertically
and horizontally polarized outputs might be expected and is often used
in similar experiments, this is not optimal. Why? Because they
don't provide much additional information compared to a single signal,
being essentially complements of each-other. Having multiple signals may help
reduce noise and eliminate offsets due to non-polarized light. However,
they don't permit the determation of the direction of rotation if the
input polarization is initially aligned with one of the polarizers
(e.g., 0, 90, 180, or 270 degrees), or make it possible to disambiguate
a change in rotation direction that may occur near one of these angles.

Therefore, in this setup, the polarizer for one of the photodiodes is
oriented at 90 degrees but the other one is oriented at 45 degrees.
Their outputs are called p and r, respectively. (The
designations p and s are for polarizations at 90 degrees to
each-other, thus the r instead of s. And, what I've called p may not
be in universal agreement with everyone's definition. So, just think
of them as two variables!) They provide quadrature signals in the
same way as in a rotary encoder, so the output rotation will
always be unambiguous. Since a full cycle of the polarization is 180
degrees rather than 360 degrees, the quadrature angle needs to be 45
degrees instead of 90 degrees but it's the same principle. (More on
the angle doubling due to Malus' law below.)

The outputs of the photodiodes (PDs) go to the two channels of an
analog scope, which unfortunately has no storage capability. This is
one time I'd prefer a digital scope or data acquisition system! The
trigger comes from a current sense resistor of 0.2 ohms, which was
also used initially to determine the actual current in the coil.
Since the scope has a "trigger view" function, the current (I) can be
displayed as a third trace, since it is already used for triggering.

With the 5 uF energy storage capacitor bank, the pulse duration is about
2.5 ms and the system is just slightly underdamped. The peak current is 12 to
13 A into a coil with a resistance of 120 ohms. Based on the dimensions
and resistance of the coil, it has approximately 2,700 turns of #32 AWG
wire, producing more than 32,000 peak A-T. (This was found using the
equations in the section: "Estimating the Number of Turns of Wire in a Coil"
in the document: "Notes on the Troubleshooting and Repair of Small Household
Appliances and Power Tools" of the
Sci.Electronics.Repair FAQ.)
However, the large number of turns results in a high inductance which is
far from ideal. A smaller number of turns of thicker wire would be much
better but scroungers can't always be too selective. For example, if
there were 1/4 the number of turns of wire with 4 times the
cross-sectional area, the resistance would be 1/16 and the current
could be 16 times larger with the ampere-turns being 4 times as large
so the magnetic field would be larger (subject to saturation effects
of the iron of the yoke). This might be a bit much for the flashlamp
from a disposable camera, but not for a larger one. Rewinding the
solenoid might be possible but the yoke is not designed to be easily
disassembled.

While the energy of the capacitor at 2,500 V is about 15 Joules, most of
this is dissipated in the coil so the flashlamp isn't being stressed. I'd
guess the dissipation there is under 1 Joule.

Plots of actual data:

Faraday Rotation from Pulsed Magnetic Field in
Kigre M18 Terbium-Doped Glass shows the results. Note that the
initial angle is 9 degrees, not 0 degrees. The total change in
rotation angle is about 134 degrees corresponding to a peak magnetic field
of about 1.1 Tesla (11,000 gauss). This is a negative of a photo taken with a
older cheap digital camera from an analog scope, thus the strange colors. :).
(The camera has no sync input or output, and no manual focus. And, to get good
contrast on the scope trace, the room had to be nearly dark - and autofocus
wouldn't work. So, with the camera on a tripod, it came down to (1) turn
the lights on to lock in focus and exposure by pressing shutter the button
halfway, (2) turn the lights off while continuing to hold the shutter button
halfway, (3) depress the shutter button fully to take the photo, (4) as soon
as the fake click of the shutter opening is heard, press the trigger button on
the pulser and hope this was done fast enough for the pulser to fire while
the shutter is still open. It worked about 2/3rds of the time.)

Using the actual value of the current of 12 A measured with the 0.2 ohm sense
resistor, the dimensions of the coil, and an estimate of the number of turns,
the resulting magnetic field is 1.3 T, which is remarkably close to the
measured value of 1.1 T considering all the assumptions and hand waving. :)
There should be inaccuracies introduced because this coil has multiple layers
and because there is an iron yoke completing part of the magnetic circuit.

The plot above shows the complete event except for the very tail of the current
pulse. The three traces are the current, I (scale on the left) and r and p
optical power (or intensity, scale on the right). A scale for signals r'
and p' (to be described below) is also provided on the right. The units
are arbitrary, based on the scope graticle. I believe the slight skew
between r and p is a combination of the linear polarizers not being oriented
at exactly 45 degrees and the beamsplitter cube transmission and reflection
being slightly polarization-dependent even though it's supposed to be
non-polarizing. The response of the M18 glass is very fast - probably
in the 100s of GHz range if not higher - so that is not an issue here
since these pulses are on the order of milliseconds.

Note that the electrical system is slightly
underdamped so the current, and rotation angle, go a bit negative near the
end. Faraday Rotation in Kigre M18 Glass - Complete
Trace shows all the gory details. (Note that this is a different shot
so the values are not quite identical.) When the current is descreasing
and crosses zero going negative, the flashlamp is still conducting. But
when the current attempts to cross zero going positive, the flashlamp
apparently cuts off and thus the glitch before it flat-lines. Note that
the magnitude of the negative current is quite small - less than 5 percent
of the peak - but since r is changing rapidly at around that point, it looks
a lot worse than it really is. The two pin connector attached to the
solenoid terminals (visible in the photo) was intended for a snubber
circuit to eliminate the undershoot, but it never was installed.

And, see Faraday Rotation in Kigre M18 Glass - Various
Starting Angles for the appearance with the a bunch of randomly
selected input polarizations, obtained by rotating the HeNe laser. :)
(No effort was made to assure that the gain and offset of the r and p
signals were exactly the same in each case, so they aren't.)
Using a Half Wave Plate (HWP) in front of the laser to set the initial
polarization angle, and for adjustment of the polarizers and detector
electronics so the signals are precisely orthogonal and have equal
gain and offset, would be better than rotating the entire laser
since it will have no effect on beam alignment. However, the HWP would
have to be closely matched to the laser wavelength to maintain pure
linear polarization.

Calculating the rotation angle:

The rotation angle can be easily obtained using Malus' law and a bit of
trigonometry. Remember that? :)

Malus' law relates the intensity of light passed by a polarizer to
the angle between a linearly polarized input beam and the polarizer,
or equivalently, to the angle between polarizers if using non-polarized
light.

I = Io*cos(theta)2

where Io is the intensity at 0 degrees and I is the actual
intensity.

With a photodiode monitoring a fixed beam profile, intensity will be
proportional to power. For the Faraday Rotation (FR) setup, there are
a pair of polarizers offset by 45 degrees producing two signals, r and p:

r = Io*[cos(theta-45)]2 and
p = Io*[cos(theta)]2

where r and p are the actual photodetector signals with a minimum value of
0 and a maximum value of Io.

Note that this assumes both signals have the same minimum value (0) and
maximum value (Io) as in the plot, above. Otherwise,
appropriate adjustments should be made to eliminate any offset(s)
and to make their scaling factor the same. I in fact did this by adjusting
the vertical channel position and gain controls on the scope before taking
the shots. This was done by rotating the laser to set the minimum and
maximum on the display to be the same for both signals. Where they
have already been captured, "adjustments" will need to be done on the data.
This is left as an exercise for the student!

Continuing on using a basic trig identity:

r = 0.5*Io*[1 + cos(2*(theta-45))] and
p = 0.5*Io*[1 + cos(2*theta)]

This angle doubling is what results in 45 degrees being the required
quadrature angle between r and p.

Or defining the halfway point for r and p and using values relative to it,
calling them r' and p', which may be intuitively easier:

r'
theta = 0.5*arctan(----)
p'

Both equations are subject to the condition that the rotation function must
be continuous. A value of +/-(n*90) or +/-(n*180) degrees may need to be
added to theta to achieve this since the arctan function can fall into the
wrong quadrant.

I used MS Excel to confirm expected behavior for the data in the plots, above.
In addition, the angles were estimated using the current trace relative to
maximum current (based on values in the plot normalized to the peak
magnetic field as determined from r' and p'). All the annotated angles
are included along with a few intermediate easy to record ones:

The values for r', p', and current (I) are from the plots and not volts
or amps! And they were only slightly fudged. :) Due to the small skew in
the r and p polarizers, I had to estimate some values where one of the
signals was changing rapidly and didn't line up with the other as expected.
In principle, I could go back and reshoot the data but that isn't going to
happen! I was also trying to reconcile my inability to match up the magnetic
field from the r and p signals compared to the magnetic field predicted by
based on current. Then I realized that there is real hysteresis in the
response of the solenoid's magnetic field with respect to the current. The
magnetic field lags behind the current. So, the actual magnetic field (from
r and p) is smaller than what would be predicted based on ampere-turns when
the current is increasing and larger when the current is decreasing.
Interesting. It's also possible that some or all of the hysteresis is
in the response of the M18 glass to the magnetic field but based on what
is found in the literature, this doesn't seem very likely.

Why the Faraday rotation experiments were done:

The reason I got involved is that a grad student at Cornell is using
the stuff to measure high magnetic fields in plasma physics experiments and I
decided I wanted to play as well. The peak magnetic fields involved in
the research are only about 50 percent greater than what I have achieved,
but the pulse duration is shorter by nearly 4 orders of magnitude. This
requires more expensive detectors, high speed data acquisition, and super
shielding in the vicinity of million amp current pulses, but
is fundamentally the same problem. I will
describe the actual details in the future. :-) But for now, see
Magnetic
Field Measurements in Wire Array Z-Pinches (Poster) and
Magnetic Field Measurements
in Wire Array Z-Pinches and X-Pinches (Paper) if you are curious.
But more recent results are far more convincing.

Laser Measurements

Laser Surveillance

The simplest type of system would use the beam from low power laser (e.g.,
red laser pointer, HeNe laser, or IR diode laser module) sent around the
perimeter of a building or in criss-cross fashion within an area to be
protected. It is best to use front surface mirrors for this but for a
reasonable number of bouces (say, less than a couple dozen), ordinary
rear surface mirrors will work just fine. However, I can usually scavange
front surface mirror bits while taking walks along highways where
fender-benders occur frequently. Automotive side-view mirrors are actually
quite decent. :)

The circuit below will activate a relay (K1) when dark. It will easily
detect a laser pointer after many bounces from mediocre mirrors, a flashlight,
100 W bulb at several feet without a lens, etc. All components are probably
available from Radio Shack, certainly from DigiKey or Mouser. The only
not totally common parts are PD1 and K1. I used a Photonic Devices, Inc.
part number PDB-V107 (about $2 from Digikey) for PD1. This has a nice large
active area of 17 mm but almost any silicon photodiode will work including
those salvaged from computer mice and barcode scanners. K1 is a low current
relay from Radio Shack but I don't know if it is still listed in their current
catalog. There is nothing critical in this circuit.

The idea is to bounce a laser beam off of a window pane and detect
vibrations from conversation or other sounds inside the room due to the
minute vibrations of the glass. (This same approach can be used to build
a laser microphone and this would be somewhat easier since the distances
are much shorter and everything is within your control.)

Basic experiements can be performed with just a laser pointer, solar cell,
and audio amp. However, keep in mind that to
really get any decent performance is not a trivial undertaking. Sound is
likely to be distorted and noisy with contributions from both inside and
outside. And just getting enough optical return off a window unless at
precisely normal incidence will be a challenge in itself.
Here is one link that appears to have rather detailed information:
Laser Microphone.

Laser Display

Ever since I first ripped apart a laser printer I've known that those
spinning mirrors and weird optics would be perfect for a laser
oscilloscope, but I didn't have any lasers powerful enough and didn't
really know where to begin, so the idea just kept rattling around in my
head. Until now. A while ago I came upon a cheapo video DVD-burner with a
fried PSU. That was the laser I'd been waiting for. And largely thanks to
this amazing site, I found out how to use it.

The thing is built around a square rotating mirror sweeping the
laser beam, a few flat lenses pulling the sweep together to about 30
degrees, and a speaker voice-coil tilting a long narrow mirror around a
hinge. Bror Westblad's Mark-I Laser Oscilloscope
Optical Path. Through the "Amplified Ear" AGC amp from
RED Free Circuit Designs, a
microphone picks up any sound in the room and displays it on a nervous red
line on the wall. The effect is quite eerie, but on a well lit gallery
wall it doesn't have quite the visual punch I was hoping for. It appears
that even a painfully bright laser spot becomes rather feeble when
stretched out to a two meter long line.

Here's all I know about the laser:
The DVD-burner was dead, so I just ripped out the optical module, and, as
it seemed people do that sort of thing, I hooked up the laser straight to
two not so peppy Duracell rabbits and, hey presto, light! Then I looked
into power supplies, and ended up building SG-LD1. That worked
perfectly when I tested it with dummy LEDs and a photodiode. But not with
the laser! The LD is an "open can" thing, which let me inspect it properly
with a 24x magnifier and, what do you know, there is nothing connected to
the PD pin! (The pin was soldered to ground/case in the unit, but I wrongfully
assumed that it just wasn't in use. Well, it wasn't even there!)

So, I ended up building that super simple LM317 PSU. And now it works. But,
I've no idea how much current I can feed the laser. The thing is, when I
turn the power up, the output increases smoothly and I don't really see any
distinct threshold. At 60 mA the output is about as bright as from a
regular 1mW laser pointer. When I initially tested the laser with the
batteries it drew 84 mA, so I guessed that to be some sort of max limit.
So, in the final assembly, I adjusted the current to 81 mA.

Conway's "Game of Life" is not really a game but a cellular automaton where
each successive generation of each point in an array is a specific function
of its local neighborhood in the previous generation. Google for "Conway's
Game of Life".

One of my students built a real time (60 iterations per second on a 512 x
512 grid) implementation using conventional video technology about 20 years
ago. When displayed in this manner, the appearance can be truly mesmerizing.

This would be a natural for a laser display. The dimensions
would not be restricted to common video formats but could be anything
reasonable. While custom digital hardware including a full frame store
had to be built 20 years ago to produce a real-time update rate, nowadays,
a modern PC may be fast enough to result in an acceptable presentation.

Laser Games

Build a covered 2-D or 3-D (or higher if your Universe supports it) maze
placing a fixed collimated laser (laser pointer, diode laser module, or HeNe
laser aimed into the maze and planar mirrors at various locations on swivel
mounts. The objective would be to adjust the mirrors so that the beam passed
through the maze and exited at some predetermined location without removing
the cover. Perhaps, peep holes could be placed at strategic locations to
help. The maze need not be Cartesian. :)

A typical front surface aluminized mirror reflects about 90 to 95 percent of
the light so there can be quite a few bounces before the beam loses so much
intensity as to be undetectable. However, the quality of the mirror is
also important so as not to distort or scatter the beam. Sources for these
mirrors include barcode scanners and laserprinters. Back surface
mirrors are considerably worse than front surface mirrors. Dielectric
mirrors coated for the specific laser wavelength are by far the best,
some reflecting 99.999 percent of the light.